{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R497",
  "content_hash": null,
  "slug": "mdsc-artifact-exact-f2-seven-census",
  "type": "artifact",
  "title": "Exact F₂⁷ census, Appendix C replay, and Singer-orbit search",
  "summary": "A standard-library Python replay enumerates every subspace of F₂⁷, reconstructs the published 333-code, closes its radius-five replacement neighborhood, and computes the full Singer-invariant compatibility graph.",
  "relevance": "For Exact mixed-dimension subspace-code number A_2(7,4), record mdsc-artifact-exact-f2-seven-census (“Exact F₂⁷ census, Appendix C replay, and Singer-orbit search”) supplies evidence or a replay used to check the packet. The record states: A standard-library Python replay enumerates every subspace of F₂⁷, reconstructs the published 333-code, closes its radius-five replacement neighborhood, and computes the full Singer-invariant compatibility graph.",
  "relevance_source": "recorded",
  "body": "Run the repository source with the stated CPython command. The script uses integer bit masks for vectors and subspace membership. Unique reduced row echelon bases enumerate all subspaces. Every distance uses exact intersection cardinalities. The Appendix C representatives and printed Klein four-group generators are embedded with attribution. The output is one canonical compact JSON object followed by LF.",
  "status": "available",
  "evidence_grade": "executable",
  "scope": {
    "kind": "bounded",
    "statement": "all 29,212 subspaces of F_2^7, the published 333-code and its radius-five neighborhood, and every orbit under the fixed Singer action",
    "bounds": {
      "ambient_subspaces": {
        "min": 29212,
        "max": 29212
      },
      "published_codewords": {
        "min": 333,
        "max": 333
      },
      "replacement_deletions": {
        "min": 0,
        "max": 5
      },
      "singer_group_order": {
        "min": 127,
        "max": 127
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "complete",
    "kind": "repository_python_exact_subspace_census",
    "command": "python3.12 tools/mixed_dimension_subspace_code_f2_7_d4_replay.py > mixed_dimension_subspace_code_f2_7_d4_replay.json",
    "entrypoint": "tools/mixed_dimension_subspace_code_f2_7_d4_replay.py",
    "runtime": "CPython 3.12.13 standard library, macOS 26.2 arm64",
    "source": "tools/mixed_dimension_subspace_code_f2_7_d4_replay.py",
    "citation": {
      "locator": "Repository artifact tools/mixed_dimension_subspace_code_f2_7_d4_replay.py at SHA-256 9797fce92dd74f099e9c342862847a0091d5b2239fe42ec372129ce6632a6ce7; Appendix C data from arXiv:1708.06224v5"
    },
    "dependencies": [
      {
        "name": "CPython standard library",
        "version": "3.12.13",
        "license": "Python-2.0"
      }
    ],
    "outputs": {
      "format": "one canonical compact JSON object followed by LF",
      "witness_digest_encoding": "UTF-8 compact JSON with sorted keys over removed_indices and added_masks_hex; the aggregate digest uses the ordered array of witness objects",
      "source_bytes": 25231,
      "source_line_count": 841,
      "source_sha256": "9797fce92dd74f099e9c342862847a0091d5b2239fe42ec372129ce6632a6ce7",
      "stdout_bytes": 3378,
      "stdout_sha256": "a7c1e04c98c69c0d7c56688d24f9d1a3928bc839f098b6266a17219b1739df18",
      "payload_sha256": "703f397d8bbc8285ddf7e31529c457d02ac65160f29b729a6e2d4811140eaa12",
      "expected": {
        "total_subspaces": 29212,
        "published_code_size": 333,
        "published_code_compatible_additions": 1,
        "radius_five_best_size": 334,
        "radius_five_removal_sets_checked": 37591,
        "radius_five_best_size_by_exact_deletions": {
          "0": 334,
          "1": 333,
          "2": 333,
          "3": 333,
          "4": 334,
          "5": 333
        },
        "radius_five_selected_optimal_witnesses_sha256": "e694fe602c2f0977efa1224876e9e61e312b1b5e9f07472e79f72849bbb0eb9f",
        "radius_five_selected_optimal_witness_sha256": [
          "0304f3fa45692ac7a9c9f28eef9168d52fa9b0d951d203411923c2ded1e1150d",
          "66251325d8f8d0d84b159fba3659ab219a80c462df87b6c8b306c43a80eb69a7",
          "76bd2b2548e30761dbc3c5c7e26eac9d12cbecd09ef9deb093b42a1c8c03002d",
          "785bfd952f91ecd1edd1c940528f982480c71e1ea83deb2617a1663d0ef96603"
        ],
        "singer_orbit_graph_vertices": 144,
        "singer_orbit_graph_edges": 72,
        "largest_fully_singer_invariant_code": 255
      }
    },
    "runtime_seconds": 6.27
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Repository artifact tools/mixed_dimension_subspace_code_f2_7_d4_replay.py at SHA-256 9797fce92dd74f099e9c342862847a0091d5b2239fe42ec372129ce6632a6ce7; Appendix C data from arXiv:1708.06224v5"
  },
  "models": [],
  "relations": [
    {
      "slug": "R499",
      "title": "Search exact mixed-dimension extensions near the published 333-code",
      "object_type": "attempt",
      "relation": "uses",
      "direction": "incoming"
    },
    {
      "slug": "R503",
      "title": "The published 333-plane code has a unique one-word extension",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "R504",
      "title": "Deleting at most five published planes still cannot beat 334",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "R498",
      "title": "Test full Singer invariance as a lower-bound route",
      "object_type": "attempt",
      "relation": "uses",
      "direction": "incoming"
    },
    {
      "slug": "R506",
      "title": "Full Singer invariance caps a mixed code at 255",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "R500",
      "title": "Extend the exact replacement search through six deletions",
      "object_type": "attempt",
      "relation": "uses",
      "direction": "incoming"
    },
    {
      "slug": "mixed-dimension-subspace-code-f2-7-d4",
      "title": "mixed dimension subspace code f2 7 d4",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}